Krichever tau-function: basic properties and modern applications
In this course I plan review what is known about quasiclassical tau-function, introduced by Igor Krichever in 1992 in the context of topological string theories. The first aim is to define it and formulate its main properties, based on some fundamental facts from the complex geometry of Riemann surfaces, mainly the Riemann bilinear identities. I am going to present some simple proofs, and discuss most important examples, which include the Seiberg-Witten prepotentials and matrix models. I am going to pay special attention to one of the most important points: the residue formula for the third derivatives of the Krichever tau-function and its relation with associativity or WDVV equations.
Finally I would like to discuss certain modern developments, related with this object, which include the relation with instanton partition functions, isomonodromic tau-dunctions and even some unexpected relations with other famous relations in mathematical physics.
Finally I would like to discuss certain modern developments, related with this object, which include the relation with instanton partition functions, isomonodromic tau-dunctions and even some unexpected relations with other famous relations in mathematical physics.
讲师
Andrei Marshakov
日期
2024年07月08日 至 12日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周一,周三,周五 | 14:20 - 16:55 | A3-4-301 | ZOOM 05 | 293 812 9202 | BIMSA |
修课要求
Complex analysis, Hamiltonian mechanics, basic knowledge of Riemann surfaces
课程大纲
1. Reminder: Riemann surfaces, Abelian differentials, Riemann bilinear identities.
2. Complex curves with Krichever data, definition of the quasiclassical tau-function.
3. Reminder: integrable systems of particles, Toda and Calogero.
4. Examples: Seiberg-Witten prepotentials and dispersionless KP theory.
5. Residue formulas for the third derivatives.
6. Residue formulas and WDVV equations, Landau-Ginzburg theories.
7. Dispersionless KP and 2d quantum gravity.
8. Modern development: instanton partition functions and isomonodromic deformations.
2. Complex curves with Krichever data, definition of the quasiclassical tau-function.
3. Reminder: integrable systems of particles, Toda and Calogero.
4. Examples: Seiberg-Witten prepotentials and dispersionless KP theory.
5. Residue formulas for the third derivatives.
6. Residue formulas and WDVV equations, Landau-Ginzburg theories.
7. Dispersionless KP and 2d quantum gravity.
8. Modern development: instanton partition functions and isomonodromic deformations.
听众
Graduate
视频公开
公开
笔记公开
公开
语言
英文